The government has raised the prospect of double-decker trains coming to British tracks on the £32bn high speed rail network set to be approved this week.

The decision by the transport secretary, Justine Greening, to go ahead with the first phase of the HS2 network from London to Birmingham is expected as early as Tuesday.

Consultants have drawn up blueprints for double-deckers up to 400 metres long, carrying more than 1,000 passengers, on the network. Supporters of high speed rail say tackling the limited capacity offered by existing lines is crucial.

Greening told the Sunday Times she was excited by the idea of "continental-style double-decker trains that immediately give you more seats and more space". The trains could have glass viewing ceilings and meeting areas.

David Cameron has reiterated his support for the project, which he says would help bring economic prosperity to the regions and bridge the north-south divide.

Yet the go-ahead will test support within the Conservative party, especially among MPs representing constituencies along the proposed route in the Chilterns. One, Cheryl Gillan, has threatened to resign as the Welsh secretary.

However, Greening is thought to be taking a more sympathetic approach to local concerns and may announce a package of additional work to mitigate noise and visible construction.

In the Chilterns, feeling still runs high over what many Tory voters see as a betrayal by their own party. Locals fear years of disruption while the line is being built, and one mitigation measure under consideration is a £500m tunnel through hills north of Amersham.

The project is unlikely to be pushed off course by any parliamentary revolt, with Labour also backing it, although prominent Labour voices have also dissented. Labour MP David Lammy told the BBC on Sunday that "questions have to asked" about the level of expenditure at a time of austerity when existing transport routes needed attention.

The biggest number of home demolitions is likely to occur in Camden, represented by Labour's Frank Dobson, where new tracks into Euston are planned on a site on which four local authority blocks currently stand.

While the shadow transport secretary, Maria Eagle, favours an alternative route via Heathrow – which was backed by the Tories in opposition – she has indicated that she will not challenge the route once it is announced. Instead, Labour will be pushing for assurances that the network will not become a separate, premium service for wealthy travellers.

Eagle said: "We need a high speed network that is affordable for the many, not the few, a network that is not a rich man's toy but one that is more than just a business class service."

At present, the Department for Transport says fares will be "comparable". Commuter fares along Britain's first high-speed line in Kent cost approximately 20%-30% more than the regular service.

The London-Birmingham route is planned to be running by 2026, with the Y-shaped network's lines to Manchester and Leeds completed by 2032.